Infragravity waves on fringing reefs in the tropical Pacific: Dynamic setup. Issue 5 (13th May 2016) - Becker, J. M.; Merrifield, M. A.; Yoon, H.
Abstract: Cross‐shore pressure and current observations from four fringing reefs of lengths ranging from 135 to 420 m reveal energetic low‐frequency (∼0.001–0.05 Hz) motions. The spatial structure and temporal amplitudes of an empirical orthogonal function analysis of the pressure measurements suggest the dominant low‐frequency variability is modal. Incoming and outgoing linear flux estimates also support partially standing modes on the reef flat during energetic events. A cross‐covariance analysis suggests that breakpoint forcing excites these partially standing modes, similar to previous findings at other steep reefs. The dynamics of Symonds et al . (1982) with damping are applied to a step reef, with forcing obtained by extending a point break model of Vetter et al . (2010) for breaking wave setup to the low‐frequency band using the shoaled envelope of the incident free surface elevation. A one parameter, linear analytical model for the reef flat free surface elevation is presented, which describes between 75% and 97% of the variance of the observed low‐frequency shoreline significant wave height for all reefs considered over a range of conditions. The linear model contains a single dimensionless parameter that is the ratio of the inertial to dissipative time scales, and the observations from this study exhibit more low‐frequency variability when the dissipative time scale is greater than the inertial time scale for the steep reefs considered. Key Points: Observations of low‐frequency motions on steep fringing reefs exhibit modal behavior A linear model with forcing derived from a point‐break model of setup describes the observations Reefs with larger dissipative than inertial time scales exhibit more low‐frequency variability